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I suspect that if someone offered you the same deal but the bet was your next 5 years income you would very rapidly come around to your friend's way of thinking.

[/ QUOTE ]Bankroll is the only valid reason there is to let this offer down. So the next 5 years income isn't really a fair proposition and most people will in fact turn it down, and not because they don't like the odds on the flip but because it's not within their bankroll.

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I disagree. The most valid reason for turning the bet down is that you are not a gambler and see no reason to risk losing $10.

It's as simple as that.

If she were offered a guaranteed, unlimited, series of similar wagers, and had the BR to handle the unlikely possibility of a run of very bad luck, then the position would be quite different.

As it is, it seems perfectly sensible to say that you can make better use of $10 100% of the time than $21 50% of the time and $0 50% of the time.

The important point is, of course, that it is pointless to talk about +EV when she's only being offered one flip of the coin.

If you are not in the habit of gambling, it really makes little difference how good the odds are (until it becomes a near certainty that you'll win). For a one off event you still risk losing your money and you may well prefer the certainty of having $10 to a 50% chance of having $21 but with a 50% chance of having sweet FA.